Algebraic Properties Worksheet for 10-Year-Olds — Math MCQ Practice (Commutative, Associative, Distributive)

Instructions

1. Read the Rules: Review the "Laws of Math Land" section to understand how numbers behave.
2. Identify the Property: For each question, look at the equation and decide which math property is being shown.
3. Solve the Problems: Complete the multiple-choice section by circling the correct letter.
4. Apply the Knowledge: Fill out the table to create your own examples of these properties.
5. Take the Challenge: Try the bonus word problem at the end!

The Laws of Math Land

Before you start, here are your four main tools for solving math mysteries:

• Commutative Property: The "Swap Rule." You can change the order of numbers when adding or multiplying, and the answer stays the same. (Example: $5 + 2 = 2 + 5$)
• Associative Property: The "Grouping Rule." You can change how numbers are grouped with parentheses when adding or multiplying. (Example: $(1 + 2) + 3 = 1 + (2 + 3)$)
• Identity Property: The "Mirror Rule." Adding $0$ to a number or multiplying a number by $1$ keeps the number exactly the same. (Example: $8 + 0 = 8$ or $8 \times 1 = 8$)
• Distributive Property: The "Sharing Rule." You multiply a single number by a group of numbers inside parentheses. (Example: $3(2 + 4) = 3 \times 2 + 3 \times 4$)

Part 1: Multiple Choice Mystery

Circle the correct answer for each question.

1. Which equation shows the Commutative Property of Multiplication?

   • A) $4 \times 1 = 4$
   • B) $3 \times 5 = 5 \times 3$
   • C) $(2 \times 3) \times 4 = 2 \times (3 \times 4)$
   • D) $6 + 0 = 6$

2. Look at this equation: $9 + (1 + 5) = (9 + 1) + 5$. Which property does this represent?

   • A) Identity Property
   • B) Distributive Property
   • C) Associative Property
   • D) Commutative Property

3. Which of these is an example of the Identity Property of Addition?

   • A) $12 + 0 = 12$
   • B) $12 \times 1 = 12$
   • C) $12 + 5 = 5 + 12$
   • D) $0 + 0 = 0$

4. What is the missing number in this Distributive Property problem? $4(3 + 2) = (4 \times 3) + (4 \times __)$

   • A) $3$
   • B) $4$
   • C) $2$
   • D) $12$

5. If $a + b = b + a$, which property is being used?

   • A) Associative
   • B) Identity
   • C) Distributive
   • D) Commutative

Part 2: Property Practice Table

In the table below, look at the property name and create your own math equation to prove you know how it works.

Part 3: Real-World Challenge

The Pizza Party Dilemma You are buying pizza for your class. You have 3 groups of students. In each group, 4 students want pepperoni and 2 students want plain cheese.

You can calculate the total number of slices using the Distributive Property: $3(4 + 2)$.

Show the two ways to solve this:

1. Add the students first, then multiply: $3 \times ( ____ ) = ____$
2. Multiply each type of student first, then add: $(3 \times 4) + (3 \times 2) = ___ + ___ = ___$

Did you get the same answer both times? (Yes / No)

Answer Key

Part 1: Multiple Choice

1. B
2. C
3. A
4. C
5. D

Part 2: Property Practice Table Examples will vary. Correct formats include:

• Associative: $(a \times b) \times c = a \times (b \times c)$
• Identity (Mult): $n \times 1 = n$
• Commutative (Mult): $a \times b = b \times a$
• Distributive: $a(b + c) = ab + ac$
• Identity (Add): $n + 0 = n$

Part 3: Real-World Challenge

1. $3 \times (6) = 18$
2. $12 + 6 = 18$ Answer: Yes